复杂无向图的同构判定方法

王卓; 王成红

doi:10.16383/j.aas.c230612

复杂无向图的同构判定方法

doi: 10.16383/j.aas.c230612

王卓^1,,
王成红^2,

1.
北京航空航天大学仪器科学与光电工程学院北京 100191
2.
中国自动化学会理事会北京 100190

基金项目: 广东省重点领域研发计划(2021B0101410005), 国家自然科学基金(61673041)资助

详细信息

作者简介:
王卓：北京航空航天大学仪器科学与光电工程学院教授. 2013年获得美国伊利诺伊大学芝加哥分校电子与计算机工程系博士学位. 主要研究方向为基于数据的系统分析与控制方法和网络理论. 本文通信作者.E-mail: zhuowang@buaa.edu.cn

王成红：中国自动化学会常务委员会研究员. 1997年获博士学位. 主要研究方向为运筹学与控制论, 图论及其应用.E-mail: chenghwang@163.com

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出版历程
- 收稿日期: 2023-10-03
- 录用日期: 2024-03-15
- 网络出版日期: 2024-05-29
- 刊出日期: 2024-06-20

Isomorphism Determination Methods for Complex Undirected Graphs

WANG Zhuo^1
,,
WANG Cheng-Hong^2
,

1.
School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191
2.
Council of Chinese Association of Automation, Beijing 100190

Funds: Supported by Key Area Research and Development Program of Guangdong Province (2021B0101410005) and National Natural Science Foundation of China (61673041)

More Information

Author Bio:
WANG Zhuo　Professor at the School of Instrumentation and Optoelectronic Engineering, Beihang University. He received his Ph.D. degree in Electrical and Computer Engineering Department, University of Illinois at Chicago, USA in 2013. His research interest covers data-based system analysis and control methods, and network theory. Corresponding author of this paper

WANG Cheng-Hong　Fellow researcher of the Council of Chinese Association of Automation. He received his Ph.D. degree in 1997. His research interest covers operational research and cybernetics, and graph theory and its applications

摘要

摘要: 针对一般复杂无向图的同构判定问题, 给出了基于邻接矩阵之和的特征多项式判定条件; 针对复杂无向连通图的同构判定问题, 给出了基于距离矩阵特征多项式和邻接矩阵特征多项式的同构判定条件, 将该条件用于复杂无向不连通图的各个连通子图, 就可解决复杂无向不连通图的同构判定问题. 上述两个判定条件均是充要条件且当复杂无向图退化为简单无向图时仍然适用.
- 复杂无向图 /
- 邻接矩阵 /
- 距离矩阵 /
- 特征多项式 /
- 同构判定条件
Abstract: For the isomorphism determination problem of general complex undirected graphs, one determination condition based on the characteristic polynomial of the sum of adjacency matrices is proposed. For the isomorphism determination problem of complex undirected connected graphs, another determination condition based on the characteristic polynomials of the distance as well as the adjacency matrices is proposed, which can also be applied to each connected subgraph of the complex undirected unconnected graph, whose isomorphism determination problem can thus be solved. The above two are both necessary and sufficient conditions and still hold true when the complex undirected graphs degenerate into simple undirected graphs.
- Complex undirected graphs /
- adjacency matrix /
- distance matrix /
- characteristic polynomials /
- isomorphism determination conditions

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图 1 例1中的各对应图

Fig. 1 Corresponding figures of Example 1

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